What is the name of this book about unicorn riders?

This was my favorite book when I was young. I believe it would have been published in the late 80s or very early 90s. It was about a girl who gets sent to another universe where she joins a band of warrior women who ride unicorns. She impresses them with modern things like orange soda and a mickey mouse watch. She learns to ride, shoot a bow and arrow and eventually helps them defeat an evil wizard. I believe it’s the first in a series, though I never read any farther. I think the title had something to do with “unicorn riders.” Any help would be greatly appreciated!